Question

3+√2/3-√2
rationalize the denominator ​

Answer 1

Answer

$= \frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ = \frac{ {(3 + \sqrt{2)} }^{2} }{ {3 }^{2} - {( \sqrt{2} ) }^{2} } \\ = \frac{ {3}^{2} + {( \sqrt{2)} }^{2} + 2 \times 3 \times \sqrt{2} }{9 - 2} \\ = \frac{9 + 2 + 6 \sqrt{2} }{7} \\ = \frac{11 + 6 \sqrt{2} }{7}$